1. Field of Invention
This invention relates to an on-off controller for a parameter, such as current, of an electrical load.
2. Description of Related Art
There are various methods of on-off control of parameters, such as current, in an electrical load. For example, the current output of a switched mode power supply or the torque output of a switched reluctance motor can be controlled by fixed off-time control or hysteresis control. These are examples of on-off or "bang-bang" controllers in which the control regime involves actuation of a switching mechanism between only the two basic states of on and off.
A switched reluctance motor is often controlled by regulating the phase current in the or each phase winding at low speed. This is referred to as current-fed control. As a practical matter, a voltage regulated supply is normally available so an intermediate current controller is used. The controller actuates power switches to apply the voltage across the or each phase winding of the machine to establish and maintain the desired phase current.
A description of switched reluctance machines and their control can be found in the article `The Characteristics, Design and Applications of Switched Reluctance Motors and Drives` by Stephenson and Blake, presented at the PCIM '93 Conference and Exhibition at Nurnberg, Germany, Jun. 21-24, 1993.
Both the transient and steady-state responses of the controller will be affected by the characteristics of the electrical load that the phase winding represents. For example, the phase circuit of a switched reluctance motor has neither a constant inductance nor a simple `motional EMF` effect. A simplified mathematical expression for the voltage across a phase circuit of a switched reluctance motor is: ##EQU1## where: v is the phase voltage
R is the phase resistance PA1 i is the phase current PA1 L is the phase inductance PA1 1 is the incremental phase inductance PA1 .omega. is the rotational speed PA1 .theta. is the rotor angle relative to the stator PA1 t is time PA1 the first term (iR) is that due to the resistive voltage drop in the phase winding; PA1 the second term (l(i,.theta.)di/dt) is proportional to the rate of change of phase current and is due to the effective inductance of the phase, i.e. the incremental inductance. This term can be seen to be non-linear in nature as the incremental inductance is a function of both current and angle. A plot showing the variation in the incremental inductance of a sample switched reluctance machine is shown in FIG. 1 of the drawings which is a graph of incremental inductance against rotor angle for various values of phase current. This shows that incremental inductance can vary by over 10 to 1 for a machine operated over a wide range of currents, for example a servo-drive; PA1 the last term of Equation 1 (i.omega..differential.L(i,.theta.)/.differential..theta.) can be seen to be proportional to the rotational speed (.omega.) and is therefore sometimes called the `motional EMF`. It arises because the phase inductance is a function of rotor angle and therefore varies with time as the machine rotates. It is also non-linear in nature and depends on how the phase inductance varies with rotor angle at a particular phase current and rotor angle. By way of illustration, FIG. 2 shows the motional EMF for a switched reluctance machine for a given speed and various values of phase current. PA1 i.sub.d is the demanded phase current PA1 .DELTA.i is the current excursion during the off time PA1 V is the DC link voltage PA1 R is the phase resistance PA1 .epsilon. is the `motional EMF` PA1 1 is the incremental inductance
The three different terms in Equation 1 may be explained as follows:
Many different types of current control schemes are used with switched reluctance machines. For example, fixed off-time current control is often used because it is capable of high bandwidth control and simple implementation. The simplicity is based on the fact that only the switch current need be monitored for feedback, as opposed to the phase winding current. Fixed off-time control functions by switching off the voltage for a prescribed period whenever the current reaches a predetermined demand level. After the off-time interval, the voltage is reapplied by actuating the switches of the converter. While the switches of the converter are non-conducting, knowledge of the phase current is not available, but in many applications this is not a disadvantage.
FIG. 3 shows the basic elements of a conventional off-time controller using a fixed off-time. The current to be monitored is fed to a current transducer 14, which can be of any known type. The output from the current transducer is passed through a noise filter 30 to remove spurious signals which may be present in the current transducer output, due to, for example, the switching action of the converter. In some commercial implementations, current transducers will have an integral noise filter. In either case, the amount of filtering is chosen so that the noise is suppressed without introducing any significant delay into the feedback signal. The output of the noise filter is a signal i.sub.f, representative of the current to be controlled. This signal is fed to a comparator 10 which also receives a signal i.sub.d representative of the demanded current. The comparator is arranged to output a signal i.sub.t which changes state when the feedback signal i.sub.f exceeds the demand signal i.sub.d.
The output of the comparator i.sub.t is applied both to the reset input of a set-reset flip-flop 22 and to a pulse generator 20 which applies a pulse to the set input of the flip-flop a fixed time, t.sub.off, after the output of the comparator 10 indicates that the load current has reached the demanded level. The output of the flip-flop is, therefore, a signal which can be used to enable a power converter or other device (not shown) so that it applies current to a load. When the current in the load reaches the demanded current, the output of the comparator changes state.
Where the load is linear, this switching strategy results in a current waveform like that shown in FIG. 4.
The rise and fall of current is depicted as linear and subject to voltages across the winding of the same magnitude but opposite polarity. With these assumptions an expression for the average current can be derived as: ##EQU2## where: i.sub.av is the average phase current over the switching cycle
The rise and fall of the current is, of course, not generally linear in practice. However, provided that the switching period is short compared with the time constant of the phase circuit, the error due to this approximation is often acceptably small.
It should be noted that, in this context, there may be a difference between the average current calculated over many switching cycles and the average current calculated over a few switching cycles. This can arise because of the nonlinearities referred to earlier or because of the demanded current changing over the phase cycle of the machine. In the description which follows, the term "average current" refers to the average over a few switching cycles.
From Equation 2 it can be deduced that the difference between the average phase current and the demanded current will vary according to the particular circuit characteristics. In many cases, the discrepancy is acceptable. When the phase current excursion from the demanded level is small, and/or an outer control loop governs the final motor output, the discrepancy can be compensated for. However, in other situations the discrepancy cannot be tolerated, for example, in applications where the phase current is required to be accurately profiled over a complete conduction cycle.
In fixed off-time current control of a non-linear electrical load, such as a phase of a switched reluctance motor, a variable error occurs in the average current. While this may be acceptable in some applications, higher performance applications will involve increasingly rapid changes in current that cannot be addressed adequately by an outer control loop because it is likely to introduce an output ripple in attempting to eradicate the error in the average current.
The same is generally true of other forms of control, such as hysteresis current control.